In recent years, in many fields such as industry, medicine and fashion, the requirements for three dimensional shape measurement have increased, in particular with the desire for non-contact measurement devices using optical means. Laser interferometers are widely used in the case of areas whose surface irregularities are in the order of micrometers (μm). However, for areas whose irregularities are 100 μm or more, another measuring means is required in place of the laser interferometer. Typical shape measuring methods in this case are a light-section method of scanning a slit shaped laser beam above the surface of an object, a moirê pattern measuring method, a grating pattern projection method, and the like. Among these, the grating pattern projection method has many advantages such as simple measurement processing, a simple device structure, high measurement precision, and the like, and is therefore suitable for three dimensional shape measurement.
FIG. 24 and FIG. 25 show the principle of three dimensional shape measurement using a grating pattern projection method. FIG. 24 is an example of the principle structure of a grating pattern projection device. A light source section 401 is constructed from a white light source and the like for lighting, such as a halogen lamp or the like, and illuminates a grating 411. In the grating 411, a plurality of linear grating patterns are formed having a predetermined pitch and predetermined transmitted light intensity distribution. The grating pattern of the grating 411 is enlarged or reduced by a projection lens 402 and projected onto an object 400 whose three dimensional shape is to be measured. The projected grating pattern is deformed (curved) according to the degree of irregularities of the object 400. Where the irregularities are small, deformation of the projected grating pattern is small, and where the irregularities are large, deformation of the projected grating pattern is large. Also, because the direction in which the grating pattern is distorted according to the direction of the irregularities is opposite thereto, the direction of the irregularities in the object 400 can be distinguished from the distortion direction of the grating pattern.
The two dimensional image of the grating pattern (hereafter referred to as ‘distorted grating pattern’) distorted according to the irregularities of the object 400 is detected by an image detecting section 404 comprising a CCD camera or the like via an image pickup lens 403 from a direction different to the projected direction. A data processing section 414 image processes the two dimensional image of the deformed grating pattern detected by the image detecting section 404 and arithmetically processes fluctuations in the intensity distribution thereof to calculate the three dimensional shape of the object 400.
When the two dimensional image of the deformed grating pattern is image processed to calculate the three dimensional shape of the object 400, a triangulation method determined by the distances and angles of the triangular shape between the grating 411, the object 400 and the image detecting section 404. FIG. 25 shows the principle of the triangulation method. In the triangular shape formed by the three axes of the projection light axis 420, monitor light axis 422 and base line axis 424, if the height of the position 426 of the object 400 is changed by Δh, the monitor light axis 422 moves in parallel to the broken line 423 and detected position in the detection plane 427 shifts by ΔX. In other words, the height difference Δh appears as the positional difference ΔX in the plane of the two dimensional image. Consequently, irregularity information of the object 400 can be calculated from fluctuations in the intensity distribution of the deformed grating pattern image. The intensity distribution at each of the pixel positions p (x,y) in the image detecting section 404 is converted to a three dimensional coordinate P (X,Y,Z) by the calculations of the triangulation method determined by the base line length L, angles θ and φ of the triangular shape.
When image processing of the deformed grating pattern is performed by the grating pattern projection device having the above structure, not only the Z coordinate of the coordinates P (X,Y,Z) of the object 400, but the X-Y coordinates of the coordinates P of the object 400 must be measured with high in-plane resolution. For that reason, it is necessary to set a specified intensity distribution with a gradient in the light intensity distribution such that a position of the projected grating pattern within one cycle can be finely distinguished. Further, since fluctuations in the intensity distribution of the deformed grating pattern image are not only affected by irregularities in the object 400 but are also affected by surface reflections on the object 400, it is necessary to detect intensity fluctuations due to irregularities only, without them being influenced by surface reflections.
In conventional grating pattern projection devices, as shown in the waveform in FIG. 26(a), the light intensity distribution for the interval P of each cycle of the grating pattern is set as a sine wave. Where a sine wave intensity distribution grating pattern is projected onto the surface of an object, the intensity distribution I(x) of the grating pattern at a position x on the object is as shown in formula (1).I(x)=B(x)+A(x) cos [φ(x)+α]  (1)
Where B(x) is bias intensity, A(x) is amplitude, and a is an initial phase. The sine wave intensity distribution grating pattern detects the phase φ(x) of each position from the intensity I(x). However, because the intensity I(x) fluctuates due to surface reflections, those surface reflections cannot be detected by a single grating pattern alone. Therefore, a plurality of grating patterns, having the same sine wave intensity distribution and with only their initial phases α changed, are projected in sequence onto the object 400, the plurality of deformed grating pattern images are detected, and the intensity distributions of the plurality of images are processed to measure the three dimensional shape. This method is called a phase shift method.
The waveforms 432, 433, 434 and 435 of the plurality of sine waves having different initial phases are shown in FIG. 26(b). The phase shift method will be explained using FIG. 26(b). The phase shift method of this example changes the initial phases α to 0, π/2, π, and 3π/2. If the intensities at the positions x of the deformed grating patterns, when the sine wave intensity distribution grating patterns of waveforms 432 to 435 are projected, are given as I0, I1, I2 and I3, their phases φ(x) are calculated by formula (2).φ(x)=arctan[(I3−I1)/(I0−I2)]  (2)
As the phase φ(x) within one cycle of a grating pattern is a value within the range of 0 to 2π, the three dimensional shape is measured from the optical arrangement shown in FIG. 24 by connecting the phases of each grating pattern in sequence.
In formula (2), the bias intensity B(x) and amplitude A(x) have been omitted. In other words, by using the phase shift method, the influence of surface reflections is not received and phases due purely to irregularities can be detected. Although the above is an example where the initial phase α of the grating pattern is changed in steps of π/2, a method of dividing one cycle of the grating pattern into three and shifting the initial phase α in steps of 2π/3 to detect three deformed grating pattern images can also be used.
Next, a conventional method of preparing a grating pattern will be shown. In an initial grating pattern projector, a grating pattern is prepared by drawing it directly on a glass substrate or film. As the deformation of the deformed grating pattern image is determined depending on the irregularities of the object 400, it is necessary for the grating pitch to be changeable in accordance with irregularities, so that the grating pitch is greater when the irregularities are larger, and less when the irregularities are smaller. Since the grating pitch and intensity distribution are fixed if the grating is drawn on a glass substrate, a number of types of grating with different grating pitches are prepared and these gratings are selected and used according to the irregularities of the object to be measured. When the phase shift method is used, the grating 411 is moved at a fixed pitch using a mechanized stage or the like.
Recently, sine wave intensity distribution grating patterns have been prepared using liquid crystal elements. Liquid crystals are elements whose transmitted light intensities change in accordance with a driving voltage, and can provide a grating pattern having adjustable grating pitch and intensity distribution by means of voltage control. An example of the electrode structure of a conventional liquid crystal grating is shown in FIG. 27. The electrodes 441 have a structure wherein a plurality of separated independent pixels are formed in a matrix shape having m number of row electrodes C1, C2, . . . Cm and n number of column electrodes R1, R2, . . . Rn. In the matrix shaped electrode structure, a signal comprising multiple voltage levels is applied to the row electrodes and column electrodes to perform time division driving.
In FIG. 28(a), transmitted light intensity characteristics with respect to the driving voltages of the liquid crystal elements are shown. The transmitted light intensity of liquid crystals changes according to the driving voltage, and has the characteristic that although the transmitted light intensity changes substantially in proportion to the driving voltage when the driving voltage is low, and the transmitted light intensity saturates when the driving voltage is increased. Given this, voltages corresponding to the light intensity of, for example, 452 at point A, 453 at point B, and 454 at point C, are applied to the liquid crystals, according to a set sine wave intensity distribution.
An example of sine wave intensity distribution is shown in FIG. 28(b). As the pixels of the liquid crystal grating are separated, it is a discrete intensity distribution in the horizontal and vertical directions due to the gaps of the liquid crystal grating. Also, it is a discrete intensity distribution to the extent that the number of gradients is low (the driving voltage step width is wide). The transmitted light intensities of each of point A, point B, and point C when driven at the voltages shown in FIG. 28(a) are 462, 463, and 464 in FIG. 28(b). In this way, voltages that become sine wave intensity distributions are set according to the voltage—transmitted light intensity characteristic of liquid crystal. Since liquid crystal gratings have discrete intensity distribution, in making the gradation of the sine wave high to make a smooth intensity distribution, the driving voltage width is set narrow. When using liquid crystal the phase shift method is realized by electrical control.
In a conventional grating pattern projector, it is necessary to make the intensity distribution of the grating pattern a sine wave. When making a sine wave intensity distribution grating pattern with liquid crystal, in order to approximate an ideal sine wave distribution, it is necessary to increase the gray level (intermediate tone intensity) gradation (normally 32 gradations or more). However, due to the non-linearity of the voltage—transmitted light intensity characteristic of liquid crystal shown in FIG. 28(a), creation of sine wave distribution with high gradation is difficult. In particular, because the change of intensity of the transmitted light with respect to the applied voltage decreases toward the maximum intensity and minimum intensity of the sine wave, the sine wave in these areas becomes distorted. Since arithmetically processing the distortion of the sine wave to correct it to an ideal sine wave is difficult, phase calculation precision is reduced by the distortion of the sine wave and three dimensional shape measurement errors increase.
Also, when detecting phase distribution of the deformed grating pattern image of the sine wave intensity distribution, the value of the sine wave intensity must be detected with high precision. Even when an ideal sine wave intensity distribution has been produced, as the change in the intensity of the sine wave is small in the proximity of the peak thereof, it is difficult to precisely detect the intensity in that area. As a result, when using the phase shift method, phase calculation errors occur due to intensity detection errors when calculating phases from formula (2), and three dimensional shape measurement errors increase. Moreover, in the case of grating patterns having low gradient sine wave intensity distribution, in-plane resolution of the deformed grating pattern decreases, therefore the in-plane resolution of the three dimensional measurement decreases.
Further, when using the conventional phase shift method by means of sine wave intensity distribution, the intensity distribution of the grating pattern is a sine wave, it is necessary to shift the initial phase of the sine wave by π/2 each time and project four times. As the grating pattern is projected four times, there is the problem of the increase in measurement time. when realizing sine wave intensity distribution by means of a liquid crystal grating, because the transmitted light intensity characteristic of the liquid crystal elements is non-linear, there is the problem that the change in intensity with respect to the change in voltage towards the peak intensity area is small compared to the intermediate intensity area of the sine wave, and the sine wave is distorted towards the peak intensity. Also, with regard to the drive signal generating the sine wave, the higher the gradation, the more complex a drive signal is required, therefore there is the problem that increasing the gradation of the sine wave is difficult.
Further, due to the sine wave distortion, phase errors occur when converting the intensity distribution p (x,y) to phase distribution φ(x,y), so there is the problem that three dimensional shape measurement errors become large. Also, there is the problem that, because trigonometric function processing is needed when converting sine wave intensities to phases, intensity data of obtained two dimensional images are standardization processed, a trigonometric table must be referred to for arctan values, and the like, the image data processing structure is complicated. Further, there is the problem that, because sine wave intensity distribution is non-linear, when calculating phases, phase calculation is necessary for each position on the image, leading to a long processing time.
Moreover, although determining the extent of distortion and correcting the sine wave distribution is permissible when the intensity distribution of the sine wave is distorted, determining the sine characteristic is difficult because the sine wave is non-linear. Also, even if the distortion of the sine wave can be determined, when correcting the intensity distribution by changing the effective voltage, the effective voltage must be changed in small steps. As a result, in actuality, the sine wave intensity distribution cannot be corrected and performing precise three dimensional shape measurement is difficult.
Further, the electrode structure of conventional liquid crystal gratings is a matrix shape wherein individual pixels are separated. The matrix shape has gaps between adjacent pixels, its effective pixel surface area is reduced (aperture rate is reduced) and its light usage efficiency is decreased. Also, the discontinuity of its intensity distribution is high because the gaps between the pixels are large, and optical noise occurs in the grating pattern. Furthermore, sine wave intensity detection errors increase due to the optical noise. As the matrix shape is time division driven, a complex drive signal having multiple potential levels is necessary. Moreover, as the liquid crystal elements are such that changes in the transmitted light intensity are non-linear with respect to changes in the drive voltage, setting the transmitted light distribution of the liquid crystals by means of the time division drive signal so as to have a sine wave intensity distribution is difficult.
Therefore, an object of the present invention is to provide a three dimensional shape measuring device using a liquid crystal grating, for solving the above problems which occur due to using a grating pattern having a sine wave intensity distribution.
Another object of the present invention is to provide a three dimensional shape measuring device with high measuring precision that prepares a grating pattern whose intensity distribution changes to a linear form, using a liquid crystal grating.
A further object of the present invention is to provide a three dimensional shape measuring device with high measuring precision, that detects phase distribution that changes to linear from only one phase image signal without performing phase shifting, whose grating pattern preparation is simple, and whose measuring time is short.
Still another object of the present invention is to provide a three dimensional shape measuring device with high measuring precision whose grating pattern preparation is simple and whose measuring time is short, by determining the non-linear characteristic of intensity distribution to correct it to a linear intensity distribution.